Scaling of the anomalous Hall effect in SrRuO$_{3}$

Abstract

We measure the anomalous Hall effect (AHE) resistivity $\rho_{xy}$ in thin films of the itinerant ferromagnet SrRuO$_{3}$. At low temperatures, the AHE coefficient $R_{s}$ varies with $\rho_{xx}^2$, and at higher temperatures, $R_{s}$ reaches a peak and then changes sign just below $T_{c}$. We find that for all films studied $R_{s}$ scales with resistivity in the entire ferromagnetic phase. We attribute the observed behavior to the contribution of the extrinsic side jumps mechanism and the intrinsic Karplus-Luttinger (Berry phase) mechanism including the effect of finite scattering rates.